No. Illuminate is only a red spell. Only the actual mana cost (which is only what's printed in the upper corner of the card, not what you actually end up paying) determines its color. Paying the blue kicker cost doesn't make it a blue spell. Now, provided that the spell actually is blue or green, Sunscape Familiar will reduce the total cost made higher by an additional cost like kicker. A kicked Jilt, for example, only costs UR if you control two Sunscape Familiars.
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
No. A spell's color is only determined by its mana cost and/or color indicator(s). The only color Illuminate has is red, no matter what other colors adiitional costs require. So Sunscape Familiar's ability doesn't apply to this spell.
Former Rules Advisor
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(The Gamers: Dorkness Rising)
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